Question

what is the effect of the difference of squares pattern on the multiplication of radicals

Answer 1

since
\[(a+b)(a-b)=a^2-b^2\] then for example
\[(2+\sqrt3)(2-\sqrt3)=4-3\]

Answer 2

and the radical is gone!

Answer 3

they're conjugates and you end up without a cross (middle) term. same thing with complex numbers

Answer 4

they can be also known as conjugates

Answer 5

This is used to simplify radical expressions that have a radical in the denominator.